Optimal control for absolutely continuous stochastic processes and the mass transportation problem
type: Item
instance of: scholarly article
title: Optimal control for absolutely continuous stochastic processes and the mass transportation problem
zbMATH Open document ID: 1030.93060
author: Toshio Mikami
published in: Electronic Communications in Probability
publication date: 2003-02-25T00:00:00Z
full work available at URL: https://eudml.org/doc/123220
full work available at URL: paper20.abs.html
review text: This paper deals with the optimal control problem for \(\mathbb{R}^d\)-valued absolutely continuous stochastic processes with given marginal distributions that arises in the mass transportation problem. Using the weak convergence method and the construction of a Markov diffusion process from a marginal distribution, the author proves the following results under appropriate conditions. 1) For \(d=1\), there exists a unique minimizer which is a non-random function of a time and an initial point. 2. For \(d> 1\), there exists a minimizer and for any minimizer \(X(\cdot)\), \(b^X(t, x):= E[(dX(t)/dt)/(t, X(t)= x)]\) does not depend on \(X(\cdot)\). Namely, minimizers satisfy the same ordinary differential equation. Moreover, applying the results to \(d= 1\), he gives a positive answer to Salisbury's problem.
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 1873771
zbMATH Keywords: absolutely continuous stochastic process
zbMATH Keywords: mass transportation problem
zbMATH Keywords: Salisbury's problem
zbMATH Keywords: Markov control
zbMATH Keywords: zero-noise limit
reviewed by: Makiko Nisio
MaRDI profile type: Publication
OpenAlex ID: W2149797755
DOI: 10.1214/ECP.V7-1061
description: scientific article; zbMATH DE number 1873771